Abstract
As known, the Klein-Gordon equation describe the behaviour of relativistic spinless particles.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Holland, P.R.: Geometry of dislocated de Broglie waves. Found. Phys. 17(4), 345–363 (1987)
Shojai, A., Shojai, F.: About some problems raised by the relativistic form of de Broglie-Bohm theory of pilot wave. Phys. Scr. 64(5), 413–416 (2001)
Shojai, F., Shojai, A.: Understanding quantum theory in terms of geometry. arXiv:gr-qc/0404102 v1 (2004)
Bertoldi, G., Faraggi, A., Matone, M.: Equivalence principle, higher dimensional Moebius group and the hidden antisymmetric tensor of quantum mechanics. Class. Quantum Grav. 17, 3965 (2000)
Brown, H., Sjöqvist, E., Bacciagaluppi, G.: Remarks on identical particles in de Broglie-Bohm theory. Phys. Lett. A 251, 229–235 (1999)
Brown, H.: The quantum potential: the breakdown of classical sympletic symmetry and the energy of localisation and dispersion. arXiv:quant-ph/9703007 (1997)
Brown, H., Holland, P.: Simple applications of Noether’s first theorem in quantum mechanics and electromagnetism. Am. J. Phys. 72(1), 34 (2004)
Dewdney, C., Horton, G.: Relativistically invariant extension of the de Broglie-Bohm theory of quantum mechanics. J. Phys. A: Math. Gen. 35(47), 10117 (2002)
Holland, P.R.: New trajectory interpretation of quantum mechanics. Found. Phys. 38, 881–911 (1998)
Holland, P.R.: Hamiltonian theory of wave and particle in quantum mechanics I: Liouville’s theorem and the interpretation of the de Broglie-Bohm theory. Nuovo Cimento B 116, 1043–1070; Hamiltonian theory of wave and particle in quantum mechanics II: Hamilton-Jacobi theory and particle back-reaction. Nuovo Cimento B 116, 1143–1172 (2001)
Holland, P.R.: Causal interpretation of Fermi fields. Phys. Lett. A 128, 9–18 (1988)
Holland, P.R.: Uniqueness of conserved currents in quantum mechanics. Ann. Phys. 12(7/8), 446–462 (2003)
Holland, P.R.: The de Broglie-Bohm theory of motion and quantum field theory. Phys. Rep. 224(3), 95–150 (1993)
Holland, P.R.: Implications of Lorentz covariance for the guidance equation in two-slit quantum interference. Phys. Rev. A 67, 062105 (2003)
Holland, P.R.: Computing the wavefunction from trajectories: particle and wave pictures in quantum mechanics and their relation. Ann. Phys. 315(2), 505–531 (2005)
Holland, P.R.: Constructing the electromagnetic field from hydrodynamic trajectories. Proc. R. Soc. A 461, 3659–3679 (2005)
Horton, G., Dewdney, C.: A non-local, Lorentz-invariant, hidden variable interpretation of relativistic quantum mechanics based on particle trajectories. J. Phys. A: Math. Gen. 34, 9871 (2001)
Horton, G., Dewdney, C.: A relativistically covariant version of Bohm’s quantum field theory for the scalar field. J. Phys. A: Math. Gen. 37, 11935 (2004)
Horton, G., Dewdney, C., Ne’eman, U.: de Broglie’s pilot-wave theory for the Klein–Gordon equation and its space-time pathologies. Found. Phys. 32(3), 463–476 (2002)
Horton, G., Dewdney, C., Nesteruk, A.: Time-like flows of energy-momentum and particle trajectories for the Klein-Gordon equation. J. Phys. A: Math. Gen. 33, 7337 (2000)
Mostafazadeh, A., Zamani, F.: Conserved current densities, localisation probabilities, and a new global gauge symmetry of Klein-Gordon fields. arXiv:quant-ph/0312078 (2003)
Mostafazadeh, A.: Quantum mechanics of Klein-Gordon-type fields and quantum cosmology. Ann. Phys. 309(1), 1–48 (2003)
Carroll, R.: Quantum Theory, Deformation, and Integrability. North-Holland, Amsterdam (2000)
Carroll, R.: Integrable systems as quantum mechanics. arXiv:quant-ph/0309159 (2003)
Carroll, R.: (X, ψ) duality and enhanced dKdV on a riemann surface. Nucl. Phys. B 502(3), 561–593 (1997)
Carroll, R.: On the whitham equations and (X, ψ) duality. Supersymmetry and integrable models. lecture notes in physics vol. 502, pp. 33–56. Springer lecture notes in physics (1998)
Faraggi, A., Matone, M.: The equivalence postulate of quantum mechanics. Int. J. Mod. Phys. A 15, 1869–2017 (2000)
Matone, M.: The cocycle of quantum Hamilton-Jacobi equation and the stress tensor of CFT. Brazilian. J. Phys. 35(02A), 316–327 (2005)
Nikolic, H.: Covariant canonical quantization of fields and Bohmian mechanics. Eur. Phys. J. C 42(3), 365 (2005)
Nikolic, H.: Bohmian particle trajectories in relativistic bosonic quantum field theory. Found. Phys. Lett. 17(4), 363–380 (2004)
Nikolic, H.: Bohmian particle trajectories in relativistic fermionic quantum field. Found. Phys. Lett. 18(2), 123–138 (2005)
Nikolic, H.: Quantum determinism from quantum general covariance. Int. J. Mod. Phys. D15(2006), 2171–2176 (2006)
Bohm, D., Hiley, B.J.: On the relativistic invariance of a quantum theory based on beables. Found. Phys. 21(2), 243–250 (1991)
Gull, S., Lasenby, A., Doran, C.: Electron paths, tunnelling and diffraction in the spacetime algebra. Found. Phys. 23(10), 1329–1356 (1993)
Hiley, B.J., Callaghan, R.E.: The Clifford algebra approach to quantum mechanics B: the Dirac particle and its relation to the Bohm approach. arXiv:1011.4033v1 [math-ph] (2010)
Kaloyerou, P.N.: The causal interpretation of the electromagnetic field. Phys. Rep. 244(6), 287–358 (1994)
Valentini, A.: Signal-locality, uncertainty, and the subquantum H-theorem. I. Phys. Lett. A 156, 5–11 (1991)
Nikolic, H.: The general-covariant and gauge-invariant theory of quantum particles in classical backgrounds. Int. J. Mod. Phys. D 12(3), 407 (2003)
Nikolic, H.: A general covariant concept of particles in curved background. Phys. Lett. B 527(1), 119–124 (2002)
Nikolic, H.: Erratum to: “a general covariant concept of particles in curved background”. Phys. Lett. B 529(3), 265 (2002)
Nikolic, H.: There is no first quantization except in the de Broglie-Bohm interpretation. arXiv:quant-ph/0307179 (2003)
Nikolic, H.: Covariant many-fingered time Bohmian interpretation of quantum field theory. Phys. Lett. A348, 166–171 (2006)
Nikolic, H.: Boson-fermion unification, superstrings, and Bohmian mechanics. Found. Phys. 39(10), 1109–1138 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 The Author(s)
About this chapter
Cite this chapter
Licata, I., Fiscaletti, D. (2014). The Quantum Potential in Particle and Field Theory Models. In: Quantum Potential: Physics, Geometry and Algebra. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-00333-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-00333-7_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-00332-0
Online ISBN: 978-3-319-00333-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)